Mullen, Uchoa, and Glatzhofer Reply:

Mullen, Kieran; Uchoa, Bruno; Glatzhofer, Daniel T.

doi:10.1103/physrevlett.116.249702

Phys. Rev. Lett.

2016

DOI: 10.1103/physrevlett.116.249702

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Mullen, Uchoa, and Glatzhofer Reply:

Kieran Mullen

Bruno Uchoa

Daniel T. Glatzhofer

Abstract: We are as interested as the the commenters [1] about the possibility of observing a Dirac loop in a real physical system. In our work [2] we showed a simple class of lattice models that possess a Dirac loop at theier Fermi level and detailed some of the physical consequences of that loop, such as the possibility of a 3D anomalous Hall effect and topological surface states in the presence of spin-orbit coupling. nodal lines. It is remarkable that these loops can occur in simple hyper-honeycomb lattices.

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Cited by 113 publications

(181 citation statements)

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“…The 3D NLS state was recently extended to the case of time-reversal invariant systems [20,21]. Three-dimensional carbon allotrope materials with a negligible SOC effect such as Mackay-Terrones crystals [20], hyperhoneycomb lattices [22], and the interpenetrated graphene network [23] were proposed to be time-reversal invariant 3D NLS. In addition, the cubic antiperovskite material Cu3PdN [24,25], Ca3P2 [26,27], non-centrosymmetric superconductor PbTaSe2 [28] and TlTaSe2 [29] were also predicted to display such exotic state.…”

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confidence: 99%

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice ^*

Lu¹,

Luo²,

Li³

et al. 2017

Chinese Phys. Lett.

103

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Recently, the concept of topological insulators has been generalized to topological semimetals, including three-dimensional (3D) Weyl semimetals, 3D Dirac semimetals, and 3D node-line semimetals. In particular, several compounds (e.g., certain three-dimensional graphene networks, Cu3PdN, Ca3P2) were discovered to be 3D node-line semimetals, in which the conduction and the valence bands cross at closed lines in the Brillouin zone. Except for the two-dimensional (2D) Dirac semimetal (e.g., in graphene), 2D topological semimetals are much less investigated. Here, we propose the new concept of a 2D node-line semimetal and suggest that this state could be realized in a new mixed lattice (we name it as HK lattice) composed by kagome and honeycomb lattices. We find that A3B2 (A is a group-IIB cation and B is a group-VA anion) compounds (such as Hg3As2) with the HK lattice are 2D node-line semimetals due to the band inversion between cation s orbital and anion pz orbital. In the presence of buckling or spin-orbit coupling, the 2D node-line semimetal state may turn into 2D Dirac semimetal state or 2D topological crystalline insulating state.

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confidence: 99%

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice ^*

Lu¹,

Luo²,

Li³

et al. 2017

Chinese Phys. Lett.

103

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“…The planar trigonal bonding of the carbon atoms is nevertheless quite robust. Simulations with Tersoff potentials [31] indicate that hyper-honeycomb allotropes of carbon atoms could be as stable, or even more stable than other metastable allotropes such as diamond. Although synthesis of this new family of carbon allotropes can be challenging, the H-0 allotrope could be synthetized in a layer by layer fashion using monofunctionalized carbon chains of atoms in the alkyne or alkynide groups [32].…”

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confidence: 99%

Line of Dirac Nodes in Hyperhoneycomb Lattices

Mullen¹,

Uchoa²,

Glatzhofer³

2015

Phys. Rev. Lett.

Self Cite

300

140

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We propose a family of structures that have "Dirac loops", closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal connectivity present in graphene, but are three dimensional. We show that their highly anisotropic and multiply-connected Fermi surface leads to quantized Hall conductivities in three dimensions for magnetic fields with toroidal geometry. In the presence of spin-orbit coupling, we show that those structures have topological surface states. We discuss the feasibility of realizing the structures as new allotropes of carbon.Introduction.− In honeycomb lattices, the existence of the Dirac point results from the planar trigonal connectivity of the sites and its sub-lattice symmetry [1]. Less well known are "Dirac loops", three dimensional (3D) closed lines of Dirac nodes in momentum space, on which the energy vanishes linearly with the perpendicular components of momentum [2]. To date there are no experimental observations of Dirac loops, and they were predicted to exist only in topological superconductors [3] and 3D Dirac semimetals [4] in which the parameters such as interactions and magnetic field are finely tuned [2].Theoretically, graphene is not the only possible lattice realization with planar trigonally connected atoms [5]. It is therefore natural to ask if there are variations on the honeycomb geometry that might produce exotic Fermi surfaces with Dirac-like excitations and topologically non-trivial states. In this Letter, we propose a family of trigonally connected 3D lattices that admit simple tight-binding Hamiltonians having Dirac loops, without requiring any tuning or spin-orbit coupling. Some of these structures lie in the family of harmonic honeycomb lattices, which have been studied in the context of the Kitaev model [7][8][9][10][11], and experimentally realized in honeycomb iridates [12]. The simplest example is the hyper-honeycomb lattice, shown in Fig. 1a.We derive the low energy Hamiltonian of this family of systems, and analyze the quantization of the conductivity and possible surface states. Even though these systems are 3D semimetals, their Fermi surface is multiply connected, with the shape of a torus, and highly anisotropic. When a magnetic field with toroidal geometry is applied, we find that the Hall conductivity is quantized in 3D at sufficiently large field. Additional spin-orbit coupling effects can create topologically protected surface states in these crystals. We claim that in the presence of spin-orbit coupling, these structures conceptually correspond to a new family of strong 3D topological insulators [13,14]. We finally discuss the experimental feasibility of realizing those structures as new allotropic forms of carbon.Tight-binding lattice.− Our discussion starts with the simplest structure, the hyper-honeycomb lattice (see Fig.

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“…These materials constitute a new class of electronic system that is intermediate between Weyl semimetals (where the Fermi surface is pointlike), and ordinary three dimensional metals (with a two dimensional Fermi surface). As such, they can support a qualitatively new phenomenology which is exciting considerable interest [5,13,14].…”

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confidence: 99%

“…Nodal-line semimetals are a new class of topological materials that has recently been proposed [1][2][3][4][5][6][7][8][9] and observed in Ca 3 P 2 [10], TlTaSe 2 [11], CaAgP and CaAgAs [12]. A Weyl-loop material is the simplest example of these systems which at a particular filling display a two-fold degenerate one-dimensional Fermi ring in the bulk (which becomes toroidal upon doping), with massless Dirac-like quasiparticles.…”

mentioning

confidence: 99%

Topological surface superconductivity in doped Weyl loop materials

Wang

Nandkishore

2017

Phys. Rev. B

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We study surface superconductivity involving the `drumhead' surface states of (doped) Weyl loop materials. The leading weak coupling instability in the bulk is toward a chiral superconducting order, which fully gaps the Fermi surface. In this state the surface also becomes superconducting, with $p+ip$ symmetry. We show that the surface SC state is "topological" as long as it is fully gapped, and the system traps Majoarana modes wherever a vortex line enters or exits the bulk. In contrast to true 2D $p+ip$ superconductors, these Majorana zero modes arise even in the "strong pairing" regime where the chemical potential is entirely above/below the drumhead. We also consider conventional $s$-wave pairing, and show that in this case the surface hosts a flat band of charge neutral Majorana fermions, whose momentum range is given by the projection of the bulk Fermi surface. Weyl loop materials thus provide access to new forms of topological superconductivity.Comment: 9 pages, 5 figure

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Mullen, Uchoa, and Glatzhofer Reply:

Cited by 113 publications

References 2 publications

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice ^*

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice ^*

Line of Dirac Nodes in Hyperhoneycomb Lattices

Topological surface superconductivity in doped Weyl loop materials

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Mullen, Uchoa, and Glatzhofer Reply:

Cited by 113 publications

References 2 publications

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice *

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice *

Line of Dirac Nodes in Hyperhoneycomb Lattices

Topological surface superconductivity in doped Weyl loop materials

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Product

Resources

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Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice ^*

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice ^*